Monge attended the Oratorian College in Beaune. This school was intended for young nobles and was run by priests. The school offered a more liberal education than other religious schools, providing instruction not only in the humanities but also in history, mathematics, and the natural sciences. It was at this school that Monge first showed his brilliance. In 1762, at the age of 16, Monge went to Lyons where he continued his education at the Collège de la Trinité. Despite being only 17 years of age at the time, Monge was put in charge of teaching a course in physics. Completing his education there in 1764, Monge returned to Beaune where he drew up a plan of the city.
The plan of Beaune that Monge constructed was to have a major influence in the direction that his career took, for the plan was seen by a member of staff at the École Royale du Génie at Mézières. He was very impressed by Monge's work and, in 1765, Monge was appointed to the École Royale du Génie as a draftsman. Of course, in this post Monge was undertaking tasks that were not entirely to his liking, for he aspired to a position in life which made far more use of his mathematical talents. However the École Royale du Génie brought Monge into contact with Charles Bossut who was the professor of mathematics there. At first Monge's post did not require him to use his mathematical talents, but Monge worked in his own time developing his own ideas of geometry.
About a year after becoming a draftsman, Monge was given a task which allowed him to use his mathematical skill to attack the task he was given. Asked to draw up a fortification plan which prevented an enemy from either seeing or firing at a military position no matter what the position of the enemy, Monge devised his own graphical method to construct such a fortification rather than use the complicated methods then available. This method made full use of the geometrical techniques which Monge was developing in his own time. His mathematical abilities were now recognised at the École Royale du Génie and it was realised that Monge was someone with exceptional abilities in both theoretical and practical subjects.